EduSahara™ Worksheet

Question 1

1.

A chord that passes through the centre of the circle is called

(i)

circumference
(ii)

semi-circle
(iii)

diameter
(iv)

radius
(v)

chord

Question 2

2.

A chord of a circle divides the whole circular region into two parts, each called a

(i)

diameter
(ii)

circumference
(iii)

major segment
(iv)

segment
(v)

centre

Question 3

3.

The segment of the circle containing the centre of the circle is called

(i)

chord
(ii)

radius
(iii)

semi-circle
(iv)

centre
(v)

major segment

Question 4

4.

Which of the following statements are true?

a)	Each radius of a circle is also a chord of the circle.
b)	Every circle has a unique centre.
c)	A line can meet a circle atmost at two points.
d)	Every circle has a unique diameter.
e)	A circle consists of an infinite number of points.

(i)

{a,b,c}
(ii)

{b,c,e}
(iii)

{d,c}
(iv)

{a,d,e}
(v)

{a,b}

Question 5

5.

Which of the following statements are true?

a)	Two semi-circles of a circle together make the whole circle.
b)	One and only one tangent can be drawn to a circle from a point outside it.
c)	Every circle has a unique diameter.
d)	An infinite number of diameters may be drawn for a circle.
e)	An infinite number of chords may be drawn for a circle.

(i)

{b,a}
(ii)

{b,a,d}
(iii)

{c,d}
(iv)

{a,d,e}
(v)

{b,c,e}

Question 6

6.

In the given triangle S is the circumcentre. If SD = 13.80 cm, find the circumference of the circumcircle

(i)

85.7 cm
(ii)

84.7 cm
(iii)

88.7 cm
(iv)

86.7 cm
(v)

87.7 cm

Question 7

7.

Find the side of the square in the following figure if the radius of the circle is 19.00 cm.

(i)

24.87 cm
(ii)

25.87 cm
(iii)

27.87 cm
(iv)

26.87 cm
(v)

28.87 cm

Question 8

8.

If a chord AB = 11 cm is drawn in a circle with radius OA = 9 cm, find its distance from the centre of the circle

(i)

5.12 cm
(ii)

6.12 cm
(iii)

9.12 cm
(iv)

7.12 cm
(v)

8.12 cm

Question 9

9.

The diameter KL of a circle with centre 'O' is perpendicular to the chord IJ. If IJ = 20.00 cm and KM = 3.62 cm, find the radius of the circle.

(i)

15.62 cm
(ii)

13.62 cm
(iii)

14.62 cm
(iv)

16.62 cm
(v)

17.62 cm

Question 10

10.

'F' and 'G' are centres of circles of radii 3 cm and 17 cm such that FG = 26 cm and 'H' is the centre of the circle of radius 'r' cm which touches the above circles externally. If ∠FHG = 90°, find 'r'

(i)

8 cm
(ii)

6 cm
(iii)

7 cm
(iv)

5 cm
(v)

9 cm

Question 11

11.

Which of the following statements are true?

a)	The radius is the shortest chord.
b)	The diameter is the longest chord.
c)	Atmost one chord can be drawn on a circle with a certain length.
d)	A chord divides a circle into two sectors.
e)	A chord divides a circle into two segments.

(i)

{a,b}
(ii)

{c,e,b}
(iii)

{d,a,b}
(iv)

{b,e}
(v)

{c,e}

Question 12

12.

Which of the following statements are true?

a)	Equal length chords are equidistant from the centre of the circle.
b)	No two chords bisects each other.
c)	The farther the chord is from the centre, the larger the angle it subtends at the centre.
d)	The longest chord of the circle passes through the centre of the circle.
e)	Equal length chords subtend equal angles at the centre of the circle.

(i)

{b,a}
(ii)

{b,c,e}
(iii)

{b,a,d}
(iv)

{a,d,e}
(v)

{c,d}

Question 13

13.

Which of the following statements are true?

a)	The area enclosed by a chord and its minor arc is called minor segment.
b)	The diameter divides the circle into two unequal parts.
c)	A sector is the area enclosed by two radii and a chord.
d)	The area enclosed by a chord and its major arc is called major segment.
e)	A circle divides the plane on which it lies into three parts.

(i)

{a,d,e}
(ii)

{b,c,e}
(iii)

{b,a,d}
(iv)

{c,d}
(v)

{b,a}

Question 14

14.

Which of the following statements are true?

a)	Two chords bisect each other.
b)	A sector is the area enclosed by two radii and a chord.
c)	The longest of all chords of a circle is called diameter.
d)	The midpoint of any diameter of a circle is its centre.
e)	The diameter divides the circle into two unequal parts.

(i)

{b,d,c}
(ii)

{a,c}
(iii)

{b,d}
(iv)

{c,d}
(v)

{e,a,c}

Question 15

15.

Which of the following statements are true?

a)	A diameter is a limiting case of a chord.
b)	A tangent is the limiting case of a secant.
c)	A radius is a limiting case of a diameter.
d)	A secant and a chord are same.
e)	A secant has two end points.

(i)

{d,b,a}
(ii)

{a,b}
(iii)

{e,c,a}
(iv)

{d,b}
(v)

{c,a}

Question 16

16.

CD , EF , GH , IJ are chords of a circle with CD = 6 cm , EF = 1 cm , GH = 5.5 cm and IJ = 6.02 cm. The chord farthest from the centre of the circle is

(i)

CD = 6 cm
(ii)

GH = 5.5 cm
(iii)

IJ = 6.02 cm
(iv)

EF = 1 cm

Question 17

17.

In the given figure, F and G are centres of two circles with equal radii intersecting at H and I. If FG = 20 cm and HI = 18.8 cm, find the radii of the circles

(i)

11.72 cm
(ii)

13.72 cm
(iii)

14.72 cm
(iv)

15.72 cm
(v)

12.72 cm

Question 18

18.

In the given figure, two circles of radii JL = 13 cm & KL = 9.5 cm intersect at L & M. The distance between the centres JK = 20 cm, find the length of LM

(i)

9.15 cm
(ii)

11.15 cm
(iii)

8.15 cm
(iv)

12.15 cm
(v)

10.15 cm

Question 19

19.

In the given figure, O is the centre of the circle. E is a point on chord CD such that CE = ED. Find ∠OEC

(i)

120°
(ii)

90°
(iii)

105°
(iv)

95°
(v)

100°

Question 20

20.

DE is a line segment and G is its mid-point. Three semi-circles are drawn with DG , GE and DE as diameters. F , H and G respectively are the centres of these semi-circles. A new circle is drawn touching these three semi-circles. Find its radius, given DF = 7 cm